Subgroups — C₅⋊D₅×D₁₀₃⋊C₃ #44525484

Order 30900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₁₀₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊(C₅⋊(D₁₀₃⋊C₃))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₁₀₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅²×C₁₀₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×D₁₀₃⋊C₃	—	5	6	no	maximal
7	C₅⋊D₅₁₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅⋊D₅×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅²×D₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅⋊(D₁₀₃⋊C₃)	—	5	6	no	—
11	D₅×C₁₀₃⋊C₃	—	5	6	no	—
12	C₅×D₁₀₃⋊C₃	D₅	1	6	yes	complemented
13	C₅²×C₁₀₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₁₀₃	—	5	6	no	—
15	C₅×C₁₀₃⋊C₃	C₂×D₅	1	6	yes	complemented
16	C₂×D₁₀₃⋊C₃	—	25	1	no	Hall
17	D₅₁₅	—	5	6	no	—
18	C₅×D₁₀₃	C₃×D₅	1	6	yes	complemented
19	D₅×C₁₀₃	—	5	6	no	—
20	C₂×C₁₀₃⋊C₃	—	25	1	no	—
21	D₁₀₃⋊C₃	—	25	1	no	—
22	D₁₀₃⋊C₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
23	C₅×C₁₀₃	C₂×C₃×D₅	1	6	yes	complemented
24	C₂×D₁₀₃	—	25	1	no	Hall
25	C₁₀₃⋊C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅⋊D₅	—	103	1	no	maximal, Hall
27	C₂×C₁₀₃	—	25	1	no	—
28	D₁₀₃	—	25	1	no	—
29	D₁₀₃	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅²	—	103	1	no	—
31	C₃×C₅⋊D₅	—	103	1	no	—
32	C₃×C₅⋊D₅	—	103	1	no	—
33	C₁₀₃	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅⋊D₅	—	103	1	no	Hall
35	C₃×C₅²	—	103	1	no	Hall
36	C₂×C₃×D₅	—	515	6	no	—
37	C₂×C₅²	—	103	1	no	—
38	C₅⋊D₅	—	103	1	no	—
39	C₅⋊D₅	D₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₅	—	103	6	no	—
41	C₃×D₅	—	515	6	no	—
42	C₃×D₅	—	515	6	no	—
43	C₅²	C₂×D₁₀₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	515	6	no	—
45	C₃×C₅	—	103	6	no	—
46	C₂²×C₃	—	2575	1	no	Hall
47	C₂×C₅	—	103	6	no	—
48	D₅	—	515	6	no	—
49	D₅	—	5	6	no	—
50	C₂×C₃	—	2575	1	no	—
51	C₂×C₃	—	2575	1	no	—
52	C₂×C₃	—	103	1	no	—
53	C₅	D₅×D₁₀₃⋊C₃	1	6	yes	complemented
54	C₂²	—	2575	1	no	Sylow
55	C₃	—	103	1	no	Sylow
56	C₂	—	2575	1	no	—
57	C₂	—	25	1	no	—
58	C₂	—	103	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₀₃	C₂²×C₃
LCS	G ▷ C₅²×C₁₀₃
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅⋊D₅×C₁₀₃⋊C₃	C₂	semidirect
2. C₅⋊(C₅⋊(D₁₀₃⋊C₃))	C₂	semidirect
3. C₅²×D₁₀₃⋊C₃	C₂	semidirect
4. C₅⋊D₅×D₁₀₃	C₃	semidirect
5. C₅²×C₁₀₃⋊C₃	C₂²	semidirect
7. C₅⋊D₅₁₅	C₂×C₃	semidirect
8. C₅⋊D₅×C₁₀₃	C₂×C₃	semidirect
9. C₅²×D₁₀₃	C₂×C₃	semidirect
12. C₅×D₁₀₃⋊C₃	D₅	semidirect
13. C₅²×C₁₀₃	C₂²×C₃	semidirect
15. C₅×C₁₀₃⋊C₃	C₂×D₅	semidirect
18. C₅×D₁₀₃	C₃×D₅	semidirect
22. D₁₀₃⋊C₃	C₅⋊D₅	direct (N × H)
23. C₅×C₁₀₃	C₂×C₃×D₅	semidirect
25. C₁₀₃⋊C₃	C₂×C₅⋊D₅	semidirect
29. D₁₀₃	C₃×C₅⋊D₅	semidirect
33. C₁₀₃	C₂×C₃×C₅⋊D₅	semidirect
39. C₅⋊D₅	D₁₀₃⋊C₃	direct (N × H)
43. C₅²	C₂×D₁₀₃⋊C₃	semidirect
53. C₅	D₅×D₁₀₃⋊C₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅⋊D₅×C₁₀₃⋊C₃	2
C₅⋊(C₅⋊(D₁₀₃⋊C₃))	2
C₅²×D₁₀₃⋊C₃	2
C₅⋊D₅×D₁₀₃	3
D₅×D₁₀₃⋊C₃	5
C₂×C₃×C₅⋊D₅	103

Subgroups — C5⋊D5×D103⋊C3 #44525484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊D₅×D₁₀₃⋊C₃ #44525484